When is a 10% gain considered riskier than a 10% loss? When the 10% loss is produced when the broad stock market lost 20%, and the 10% gain occurred when the market rose 20%.

Why does that follow? Because, as defined by some financial advisers and other investment professionals, risk relates to lagging the market â ânegative alpha,â in technical-speak.

You might think that itâs absurd to consider a 10% gain as being riskier than a 10% loss. But that just means youâre using a different definition of risk: The possibility of loss.

Welcome to the complicated world of defining risk.

How about this: Which of the following two investments of $100 is preferable?

â¢ One guaranteed to earn you $1 on your original $100, for a total of $101.

â¢ One with 50% probability of your pocketing another $102, for a total of $202, and 50% probability of a total loss.

Notice that both investments have an expected value of $101. (In the second case, the expected value is equal to the average of $202 and zero.)

Notice also that the second proposition is far riskier than the first. But according to at least some valuation models, the second one is worth more than the first. Thatâs because volatility sometimes can work in your favor, allowing you to exit an investment at an unexpectedly high price.

These valuation models play havoc with the third definition of risk: volatility. Now risk is to be preferred rather than avoided.

No wonder that even the experts are often confused about investorsâ risk preferences. Itâs hard not to be confused when there are such varied, and often contradictory, definitions of risk.

The confounding effects of holding period

As if this wasnât confusing enough, peopleâs perception of risk changes as we focus on longer or shorter holding periods.

Consider the standard belief that stocks are riskier than bonds, as measured by the volatility of returns. This hardly seems controversial, but itâs also wrong when we focus on long-enough holding periods.

This is illustrated in the accompanying chart, below. Look first at the first pair of columns, which reflect the variability of all one-year holding periods since 1926. Notice that, as expected at this time horizon, stocks are far more volatile than long-term bonds; the standard deviation of stocksâ one-year returns is 16.6%, versus 9.9% for long-term bonds. Notice furthermore that this pattern is repeated when we expand our focus to five-year and 10-year holding periods: Stocksâ returns over those periods continue to be more volatile than long-term bonds.

At 20-year holding periods, however, this pattern disappears. Now the volatility of stocksâ returns is slightly lower than that of bonds.

In other words, even when using the same definition of risk, we reach different conclusions depending on the holding period.

Investment implications

If risk is so inscrutable, how do you go about assessing whether a strategy is appropriate?

As this discussion suggests, there is no one answer. I suspect that this is why Benjamin Graham, the father of fundamental analysis, made what otherwise is a very surprising claim in his investment classic The Intelligent Investor. He wrote that âthe best way to measure your investing success is not by whether youâre beating the market, but by whether youâve put in place a financial plan and a behavioral discipline that are likely to get you where you want to go.â

My interpretation of what he is telling us: Rather than engage in the endless debate over which definition of risk is the best, it would be more helpful to spend your energy determining if a strategy youâre considering is one that you can live with through thick and thin. If you canât, then it isnât appropriate for you, no matter how risky or conservative it might be according to some academic definition.

For more information, including descriptions of the Hulbert Sentiment Indices, go to The Hulbert Financial Digest or email mark@hulbertratings.com .